The tag has no usage guidance.

learn more… | top users | synonyms

-3
votes
2answers
309 views

The number of totatives to the nth primorial, in an interval shorter than the nth primorial

(The notation of this question will be improved over the next few days, sorry for the lack of clarity at the moment.) Can, and if so when can, we determine the amount of natural numbers which are ...
21
votes
2answers
1k views

Drawing natural numbers without replacement.

Suppose we start with an initial probability distribution on $\mathbb{N}$ that gives positive probability to each $n$. Let's call this random variable $X_1$ so we have $P(X_1=n)=p_{1,n}>0$ for all ...
4
votes
2answers
291 views

Relative-totient function (2nd attempt)

Let $\Lambda(x,y)$ be the count of totatives of $x$ that are less than or equal to $y$. I am asking for the following result to be verified, (particularly the final proposal), I have found no ...
7
votes
2answers
2k views

Convergence of moments implies convergence to normal distribution

I have a sequence $\{X_n\}$ of random variables supported on the real line, as well as a normally distributed random variable $X$ (whose mean and variance are known but irrelevant). I know that the ...
4
votes
0answers
201 views

Asymptotic estimate for a random model of primes

Question Let $$ \pi_{rm_c}(x) = \sum_{ \substack{ {n\leq x}\\{(n+a,P(\sqrt{n}))=1}}} 1-1, $$ where $P(x)$ is the product of all primes less or equal to $x$ and $a$ is a random integer constrained to ...
3
votes
0answers
131 views

Reference request: Darboux properties of real-valued set functions (measures, densities, etc.)

Fix a set $S$ and let $f: \mathcal P(S) \rightharpoonup \mathbf R$ be a real-valued partial function on the power set of $S$; denote by $\mathcal D$ the domain of $f$. We say that $f$ has: (i) the ...
-1
votes
1answer
197 views

Counting number of primorial factors

Denote $$P(n)=\prod_{p\in\mathsf{Primes}\leq n}p$$ signifying $n^{\mbox{th}}$ primorial. We know that $P(n)$ has approximately $n/\log2$ bits ...